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Effects of background risks on cautiousness with an application to a portfolio choice problem

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  • Hara, Chiaki
  • Huang, James
  • Kuzmics, Christoph

Abstract

We provide necessary and sufficient conditions on an individual's expected utility function under which any zero-mean idiosyncratic risk increases cautiousness (the derivative of the reciprocal of the absolute risk aversion), which is the key determinant for this individual's demand for options and portfolio insurance.

Suggested Citation

  • Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2011. "Effects of background risks on cautiousness with an application to a portfolio choice problem," Journal of Economic Theory, Elsevier, vol. 146(1), pages 346-358, January.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:1:p:346-358
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    References listed on IDEAS

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    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Franke, Gunter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1998. "Who Buys and Who Sells Options: The Role of Options in an Economy with Background Risk," Journal of Economic Theory, Elsevier, vol. 82(1), pages 89-109, September.
    3. Brennan, M.J. & Solanki, R., 1981. "Optimal Portfolio Insurance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(03), pages 279-300, September.
    4. Leland, Hayne E, 1980. " Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    5. Miles S. Kimball, 1991. "Precautionary Motives for Holding Assets," NBER Working Papers 3586, National Bureau of Economic Research, Inc.
    6. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    7. Marti G. Subrahmanyam & Günter Franke & Richard C. Stapleton, 1998. "Who Buys and Who Sells Options: The Role and Pricing of Options in an Economy with Background Risk," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-063, New York University, Leonard N. Stern School of Business-.
    8. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-920, June.
    9. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    10. Chevallier, Eric & Müller, Heinz H., 1994. "Risk Allocation in Capital Markets: Portfolio Insurance, Tactical Asset Allocation and Collar Strategies," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(01), pages 5-18, May.
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    Citations

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    Cited by:

    1. Gollier, Christian & Kimball, Miles S., 2018. "Toward a Systematic Approach to the Economic Effects of Risk: Characterizing Utility Functions"," TSE Working Papers 18-909, Toulouse School of Economics (TSE).
    2. Huang, Hung-Hsi & Wang, Ching-Ping, 2013. "Portfolio selection and portfolio frontier with background risk," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 177-196.
    3. James Huang & Richard Stapleton, 2017. "Higher-order risk vulnerability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 387-406, February.
    4. Huang, James, 2014. "Convex and decreasing absolute risk aversion is proper," Economics Letters, Elsevier, vol. 125(1), pages 123-125.
    5. repec:eee:apmaco:v:276:y:2016:i:c:p:284-296 is not listed on IDEAS
    6. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.

    More about this item

    Keywords

    Risk aversion Risk tolerance Cautiousness Portfolio insurance Idiosyncratic risks Background risks Incomplete markets;

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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